A088116 Let n = abc..., where a, b, c, are digits of n. a(n) = a*bc...+b*ac...+c*ab...+..., i.e., a(n) = sum, over all the digits, of the product (number obtained by deleting a digit multiplied by the deleted digit).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 0, 14, 28, 42, 56, 70, 84, 98

Offset

0,12

Comments

First 100 terms (for all two digit numbers) match with that of A069816. A088116(10a + b) = 2ab = (a+b)^2 - (a^2 + b^2) = A069816(10a + b).

The first known fixed points, after zero, are numbers of the forms 36*10^k and 1314*10^k for k >= 0. All have 9 as the sum of their digits. Calculated up to n = 10^10. - Stéphane Rézel, Jul 31 2019

Links

Jinyuan Wang, Table of n, a(n) for n = 0..10000

Example

a(1234) = 234 + 2*134 + 3*124 + 4*123 = 1366.

Mathematica

Join[{0}, Table[Total[IntegerDigits[n]Table[FromDigits[Drop[ IntegerDigits[ n], {d}]], {d, IntegerLength[n]}]], {n, 100}]] (* Harvey P. Dale, Dec 23 2021 *)

Prog

(PARI) a(n) = {v=digits(n); sum(k=1, #v, v[k]*(n\10^(#v-k+1)*10^(#v-k)+n%10^(#v-k))); } \\ Jinyuan Wang, Aug 01 2019

Crossrefs

Cf. A069816, A087346, A088117.

Sequence in context: A241142 A271907 A069816 * A100817 A074157 A076309

Adjacent sequences: A088113 A088114 A088115 * A088117 A088118 A088119

Keyword

base,easy,nonn

Author

Amarnath Murthy, Sep 25 2003

Extensions

More terms from David Wasserman, May 10 2005

Offset 0 from Stéphane Rézel, Jul 31 2019

Status

approved